An Empirical Potential Energy Function for Phospholipids: Criteria for Parameter Optimization and Applications

  • Michael Schlenkrich
  • Jürgen Brickmann
  • Alexander D. MacKerellJr.
  • Martin Karplus


Lipid membranes are an essential component of all living cells. A molecular description of the structure and dynamics of such membranes from either experimental or theoretical approaches is still lacking. This is due in part to the two-dimensional fluid character of membranes (Singer and Nicolson, 1972), which makes difficult a detailed analysis by X-ray diffraction, neutron diffraction, or nuclear magnetic resonance. Detailed structural data of lipid molecules based on X-ray crystallography are available only for the nearly anhydrous crystalline state (Pascher et al, 1992; Small, 1986).


Dihedral Angle Aliphatic Chain Potential Energy Function Sodium Dodecyl Sulfate Micelle Partial Atomic Charge 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aue DH, Webb HM, Bowers MT (1976): A thermodynamic analysis of solvation effects on the basicities of alkylamines. An electrostatic analysis of substituent effects. J Am Chem Soc 98:318–329CrossRefGoogle Scholar
  2. Bayly CI, Cieplak P, Cornell WD, Kollman PA (1993): A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: The RESP model. J Phys Chem 97:10269–10280CrossRefGoogle Scholar
  3. Berg RW (1977): The vibrational spectrum of the normal and perdeuterated tetramethylammonium ions. Spectrochim Acta 34A:655–659Google Scholar
  4. Blom CE, Günthard HH (1981): Rotational isomerism in methylformate and methylacetate: A low-temperature matrix infrared study using thermal molecular beams. Chem Phys Lett 84:267–271CrossRefGoogle Scholar
  5. Bottger GL, Geddes AL (1965): The infrared spectra of the crystalline tetramethylammonium halides. Spectrochim Acta 21:1701–1708CrossRefGoogle Scholar
  6. Boyd RH (1969): Lattice energies and hydration thermodynamics of tetra-alkylammonium halides. J Chem Phys 51:1470–1474CrossRefGoogle Scholar
  7. Briggs JM, Nguyan TB, Jorgensen WL (1991): Monte Carlo simulations of liquid acetic acid and methyl acetate with the OPLS potential functions. J Phys Chem 95:3315–3322CrossRefGoogle Scholar
  8. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983): CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4:187–217CrossRefGoogle Scholar
  9. Brun TO, Curtiss LA, Iton LE, Kleb R, Newsam JM, Beyerlein RA, Vaughn DEW (1987): Inelastic neutron scattering from tetramethylammonium cations occluded with zeolites. J Am Chem Soc 109:4118–4119CrossRefGoogle Scholar
  10. Charifson PS, Hiskey RG, Pedersen LG (1990): Construction and molecular modeling of phospholipid surfaces. J Comp Chem 11:1181–1186CrossRefGoogle Scholar
  11. Chirlan LE, Francl MM (1987): Atomic charges derived from electrostatic potentials: A detailed study. J Comp Chem 8:894–905CrossRefGoogle Scholar
  12. Cook RL, DeLucia FC, Helminger P (1974): Molecular force field and structure of water: Recent microwave results. J Mol Spect 53:62–76CrossRefGoogle Scholar
  13. Damodaram KV, Merz KM Jr, Gaber BP (1992): Structure and dynamics of the di-lauroylphosphatidylethanolamine lipid bilayer. Biochemistry 31:7656–7664CrossRefGoogle Scholar
  14. Dutta PK Del Barco B, Shieh DC (1986): Raman spectroscopic studies of the tetra-methylammonium ion in zeolite cages. Chem Phys Lett 127:200–204CrossRefGoogle Scholar
  15. Elder M, Hitchcock P, Mason R, Shipley GG (1977): A refinement analysis of the crystallography of the phospholipid, 1,2-dilauroyl-DL-phosphatidylethanolamine, and some remarks on lipid-lipid and lipid-protein interactions. Proc R Soc Lond A 354:157–170CrossRefGoogle Scholar
  16. Florian J, Johnson BG (1994): Comparison and scaling of hartree-fock and density functional harmonic force fields. 1. Formamide monomer. J Phys Chem 98:3681–3687CrossRefGoogle Scholar
  17. Frisch FMJ, Head-Gordon M, Trucks GW, Foresman JB, Schlegel HB, Raghavachari K, Robb M, Binkley JS, Gonzalez C, Defrees DJ, Fox DJ, Whiteside RA, Seeger R, Melius CF, Baker J, Martin RL, Kahn LR, Stewart JJP, Topiol S, Pople JA (1990): Gaussian 90 (computer program). Revision. Pittsburgh, PA: Gaussian, Inc.Google Scholar
  18. Gao J, Jorgensen WL (1992): personal communicationGoogle Scholar
  19. Gelin BR, Karplus M (1975): Role of structural flexibility in conformational calculations. Application to acetylcholine and /3-methylacetylcholine. J Am Chem Soc 97:6996–7006PubMedCrossRefGoogle Scholar
  20. Guyan L, Brady J (1996): All-hydrogen empirical force field parameters for carbohydrates. (Manuscript in preparation)Google Scholar
  21. Hariharan PC, Pople JA (1972): The effect of d-functions on molecular orbital energies for hydrocarbons. Chem Phys Lett 66:217–219CrossRefGoogle Scholar
  22. Häuser H, Pacher I, Sundeil S (1980): Conformation of phospholipids: Crystal structure of a lysophosphatidylcholine analogue. J Mol Biol 137:249–264PubMedCrossRefGoogle Scholar
  23. Häuser H, Pascher I, Pearson RH, Sundeil S (1981): Preferred conformation and molecular packing ofphosphatidylethanolamine and phosphatidylcholine. Biochim Biophys Acta 650:21–51PubMedGoogle Scholar
  24. Heller H, Schaefer M, Schulten K (1993): Molecular dynamics simulation of a bilayer of 200 lipids in the gel and in the liquid-crystal phases. J Phys Chem 97:8343–8360CrossRefGoogle Scholar
  25. Hitchcock PB, Mason R, Thomas KM, Shipley GG (1974): Structural chemistry of 1,2 dilauroyl-DL-phosphatidylethanolmaine: molecular conformation and intermolecular packing of phospholipids. Proc Natl Acad Sci USA 71:3036–3040PubMedCrossRefGoogle Scholar
  26. Hollenstein H, Günhthard HH (1980): A transferable valence field for polyatomic molecules. J Mol Spec 84:457–477CrossRefGoogle Scholar
  27. Hussin A, Scott HL (1987): Density and bonding profiles of interbilayer water as a function of bilayer separation: A Monte Carlo study. Biochim Biophys Acta 897:423–430CrossRefGoogle Scholar
  28. Jorgensen WL (1986): Optimized intermolecular potential functions for liquid alcohols. J Phys Chem 90:1276–1284CrossRefGoogle Scholar
  29. Jorgensen WL (1983): Theoretical studies of medium effects on conformational equilibria. J Phys Chem 87:5304–5312CrossRefGoogle Scholar
  30. Jorgensen WL, Swenson CJ (1985): Optimized intermolecular potential functions for amides and peptides. Structure and properties of liquid amides. J Am Chem Soc 107:569–578CrossRefGoogle Scholar
  31. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML (1983): Comparison of simple potential functions for simulating liquid water. J Chem Phys 79:926–935CrossRefGoogle Scholar
  32. Kuczera K, Wiorkiewicz-Kuczera J, Karplus M (1993): MOLVIB: Program for Vibrational Spectroscopy, Program Charmm (computer program). Version 22Google Scholar
  33. Kuczera K, Gao J, MacKerell AD Jr, Karplus M (1996): Empirical parameters for the ionic species of amino acids and protein termini. (Manuscript in preparation)Google Scholar
  34. MacKerell AD Jr (1994): Empirical force field parameters for sulfate and methylsulfate. (unpublished)Google Scholar
  35. MacKerell AD Jr (1995): Molecular dynamics simulation analysis of a sodium dodecyl sulfate micelle in aqueous solution: Decreased fluidity of the micelle hydrocarbon interior. J Phys Chem 99:1846–1855CrossRefGoogle Scholar
  36. MacKerell AD Jr, Karplus M (1991): Importance of attractive van der Waals contributions in empirical energy function models for the heat of vaporization of polar liquids. J Phys Chem 95:10559–10560CrossRefGoogle Scholar
  37. MacKerell AD Jr, Karplus M (1996a): Allatom empirical energy function for simulations of peptides and proteins. (Manuscript in preparation)Google Scholar
  38. MacKerell AD Jr, Karplus M (1996b): Parameterization of histidine for molecular modeling and molecular dynamics simulations. (Manuscript in preparation)Google Scholar
  39. MacKerell AD Jr, Bashford D, Bellott M, Dunbrack RL Jr, Field MJ, Fischer S, Gao J, Guo H, Ha S, Joseph D, Kuchnir L, Kuczera K, Lau FTK, Mattos C, Michnick S, Ngo T, Nguyen DT, Prodhom B, Roux B, Schlenkrich M, Smith J, Stote R, Straub J, Wiorkiewicz-Kuczera J, Karplus M (1992): Self-consistent parameterization of biomolecules for molecular modeling and condensed phase simulations. Biophys J 6:A143Google Scholar
  40. MacKerell AD Jr, Wiorkiewicz-Kuczera J, Karplus M (1995): An all-atom empirical energy function for the simulation of nucleic acids. J Amer Chem Soc: 117:11946 – 11975CrossRefGoogle Scholar
  41. MacKerell AD Jr, Field MJ, Fischer S, Watanabe M, Karplus M (1996): All-hydrogen alkane potential for use in aliphatic groups of macromolecules. (Manuscript in preparation)Google Scholar
  42. Mahendra P, Agarwal A, Khandelwal DP, Bist HD (1984): Dynamic disorder of (CH3)4N+ in (CH3)4NX (X = Cl, Br and I) as studied by Raman spectroscopy. J Mol Struct 112:309–316CrossRefGoogle Scholar
  43. Mahendra P, Raghuvanshi GS, Bist HD (1982): Vibrational studies and phase transitions in tetramethylammonium chloride. Chem Phys Lett 92:85–92CrossRefGoogle Scholar
  44. Mannig J, Klimkowski VJ, Siam K, Ewbank JD, Schäfer L (1986): Ab initio structural investigation of methyl and ethyl carbamate and carbamy choline. J Mol Struct (THEOCHEM) 139:305–314CrossRefGoogle Scholar
  45. Marrink S-J, Berendsen HJC (1994): Simulation of water transport through a lipid membrane. J Phys Chem 98:4155–4168CrossRefGoogle Scholar
  46. Millero FJ (1971): The molal volumes of electolytes. Chem Rev 71:147–176CrossRefGoogle Scholar
  47. Möller P, Plesset MS (1934): Note an an approximation treatment for many-electron systems. Phys Rev 46:618–622CrossRefGoogle Scholar
  48. Moravie RM, Coret J, (1974): Conformational behaviour and vibrational spectra of methyl propionate. Chem Phys Lett 26:210–214CrossRefGoogle Scholar
  49. Neria E, Fischer S, Karplus M (1996): Simulation of activation free energies in molecular systems. J Chem Phys (Submitted)Google Scholar
  50. Pascher I, Lundmark M, Nyholm P-G, Sundeil S (1992): Crystal structures of membrane lipids. Biochem Biophys Acta 1113:329–373CrossRefGoogle Scholar
  51. Pearson RH, Pascher I (1979): The molecular structure of lecithin dihydrate. Nature 281:499–501PubMedCrossRefGoogle Scholar
  52. Rao BG, Singh UC (1989): Hydrophobic hydration: A free energy perturbation study. J Am Chem Soc 111:3125CrossRefGoogle Scholar
  53. Reiher WE III (1985): Theoretical studies of hydrogen bonding (dissertation). Cambridge, MA: Harvard UniversityGoogle Scholar
  54. Roux B (1990): Theoretical study of ion transport in the gramicidin a channel (dissertation). Cambridge, MA: Harvard UniversityGoogle Scholar
  55. Schlenkrich M (1992): Entwicklung und anwendung eines kraftfeldes zur simulation von phospholipidmembransystemen (dissertation). Darmstadt, Germany: Technischen HochschuleGoogle Scholar
  56. Singer SJ, Nicolson GL (1972): The fluid mosaic model of the structure of cell membranes. Science 175:720–731PubMedCrossRefGoogle Scholar
  57. Singh UC, Kollman PA (1984): An approach to computing electrostatic charges for molecules. J Comp Chem 5:129–145CrossRefGoogle Scholar
  58. Small DM (1986): The physical chemistry of lipids. New York: PlenumGoogle Scholar
  59. Stote RH, States DJ, Karplus M (1991): On the treatment of electrostatic interactions in biomolecular simulation. Chimie Physique 88:2419–2433Google Scholar
  60. Stouch TR, Ward KB, Altieri A, Hagler AT (1991): Simulations of lipid crystals: Characterization of potential energy functions and parameters for lecithin molecules. J Comp Chem 12:1033–1046CrossRefGoogle Scholar
  61. Timmermans J (1950): Physico-Chemical Constants of Pure Organic Compounds. Elsevier: AmsterdamGoogle Scholar
  62. Venable RM, Zhang Y, Hardy BJ, Pastor RW (1993): Molecular dynamics simulations of a lipid bilayer and of hexadecane: An investigation of membrane fluidity. Science 262:223–226PubMedCrossRefGoogle Scholar
  63. Vegard L, Sollesnes K (1927): Structure of isomorphic substances N(CH3)4X. Phil Mag 4:985–1001Google Scholar
  64. Weiner SJ, Kollman PA, Nguyen DT, Case DA (1986): An all atom force field for simulations of proteins and nucleic acids. J Comp Chem 7:230–252CrossRefGoogle Scholar
  65. Wiberg KB, Laidig KE (1987): Barriers to rotation adjacent to double bonds. 3. The C—O barrier in formic acid, methyl formate, acetic acid, and methyl acetate. The origin of ester and amide “Resonance”. J Am Chem Soc 109:5935–5943CrossRefGoogle Scholar
  66. Wiberg KB, Laidig KE (1988): Acidity of (Z)- and (E)-methyl acetates: Relationship of meldrum’s acid. J Am Chem Soc 110:1872–1874CrossRefGoogle Scholar
  67. Williams G, Owen NL, Sheridan J (1971): Spectroscopic studies of some substituted methyl formates. Trans Faraday Soc 67:922–949CrossRefGoogle Scholar
  68. Woolf TB, Roux B (1994a): Conformational flexibility of o-phosphorylcholine and o-phosphorylethanolamine: A molecular dynamics study of solvation effects. J Am Chem Soc 116:5916–5926CrossRefGoogle Scholar
  69. Woolf TB, Roux B (1994b): Molecular dynamics simulation of the gramicidin channel in a phospholipid bilayer. Proc Natl Acad Sci USA 91:11631–11635PubMedCrossRefGoogle Scholar
  70. Wyckof RWG (1928): The crystal structure of tetramethylammonium halides. Z Kristallogr 67:91–105Google Scholar

Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Michael Schlenkrich
  • Jürgen Brickmann
  • Alexander D. MacKerellJr.
  • Martin Karplus

There are no affiliations available

Personalised recommendations